- #1

SweetBabyLou

- 6

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Its review time again for another Thermodynamics midterm. As such, I have a practice exam to try for optional extra review work. I've come across a problem that I'm somewhat stumped on. I've tried the problem, but I feel as though I've made too many assumptions in trying to solve the problem. Here's what I got

## Homework Statement

Air, an ideal gas, with temperature-dependent heat capacities, is to be compressed from 100 kPa to 1500 kPa. The air enters the compressor at a temperature of 300K, and the compressor has an isentropic efficiency of 85%.

How much power is required to operate the compressor adiabatically using an inlet air flow rate of 2.0 m

^{3}/s? (Calculate Power in kW)

## Homework Equations

p

_{1}= 100 kPa

T

_{1}= 300 K

p

_{2}= 1500 kPa

T

_{2}= ?

η

_{isentropic}=.85

m

_{in}= 2.0m

^{3}/s

## The Attempt at a Solution

To start the equation off, I set up the relation p

_{2}/p

_{1}= p

_{r2}/p

_{r1}

The problem gave us values for both p

_{1}and p

_{2}.

I looked up the value of temperature-dependent p

_{r1}which turned out to be:

p

_{r1}= 1.3860

While I was looking at the air tables, I also took the enthalpy value at 300K, which turned out to be:

h

_{1}= 300.19

I plugged p

_{r1}into the pressure/pressure-reduced relationship, found p

_{r2}to come out to 20.79, roughly the 20.64 found at 640K on the same air table. From this, I pulled the secong enthalpy value:

h

_{2s}= 649.22

From here, I try to solve for h

_{2}I set up the equation for isentropic efficiency:

η = (h

_{1}- h

_{2})/(h

_{1}- h

_{2s})

Solving for h

_{2}, I get:

h

_{2}= 596.8655

Finally, I solve for power.

The equation I use is:

[itex]\dot{Q}[/itex] - [itex]\dot{W}[/itex] + (m

_{i}(h

_{i})-m

_{e}(h

_{e})

**I canceled out the kinetic and potential energy terms of the original equation**

Since the process is adiabatic, I eliminate the [itex]\dot{Q}[/itex].

__Here's where I think I may have gone wrong__I then assume that the process is running at steady state, thus m

_{i}= m

_{e}= 2.0m

^{3}/s

Plugging 2 in for m and the rest of the values in for h

_{i}, h

_{e}, I find that [itex]\dot{W}[/itex] = -593.351kW

...this CAN'T be right. I'm quite possibly doing this whole problem wrong. Thus, I turn to the almighty physicsforums.com for help. I know this problem and my solution might be long-winded, so I appreciate all patience with this problem in advance. I also DEFINITELY appreciate any and all help/advice sent my way.

Thank you for your time

-Lou